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Alice's Adventures in Wonderland and Through the Looking Glass

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The second (after Jargon File) classical neo-programming book that is available from the WEB. Contains a lot of insights into crazy world of programming and system administration ;-). It can be viewed as asprecursor to the theratre of absurd ( Alice in Wonderland as a precursor to the theatre of the absurd)

Lewis Carroll's Alice books, "Alice's Adventures in Wonderland" and its sequel, "Through the Looking-Glass and What Alice Found There", are widely regarded as masterpieces of children's literature today, despite having been written more than a century ago. The timeless appeal of Carroll's works lies in his fantastical and whimsical characters, and the Alice books remain popular with both adults and children. Underlying Carroll's portrayal of Wonderland's peculiar characters, however, are elements of the Theatre of the Absurd. The themes that emerge in the Alice books bear many similarities to those explored by the playwrights in the Theatre of the Absurd, despite the separation of a century between the time of Carroll's works and the rise of the Theatre of the Absurd. This paper explores the prevalent themes in the Alice books, and examines how they may be interpreted as a precursor of Absurdist literature. The Alice books will be discussed in relation to Samuel Beckett's "Waiting for Godot", with regard to the common themes of time, memory and language, that are prevalent in both Carroll's and Beckett's works. Time is a recurring theme in the Alice books and "Waiting for Godot". In addition, both Carroll and Beckett explore similar issues of memory, albeit in counterpoint. Finally, "Waiting for Godot" reveals the devaluation of language, which Carroll also addresses.

Lewis Carroll (1832-1898), the pen name of Oxford mathematician, logician, photographer and author Charles Lutwidge Dodgson, is famous the world over for his fantastic classics "Alice's Adventures in Wonderland," "Through the Looking Glass," "The Hunting of the Snark," "Jabberwocky," and "Sylvie and Bruno." The books contain many mathematical and political allegories ( The hidden math behind Alice in Wonderland )

Though others had looked for political and social allusions in the Alice books, most notably Martin Gardner, whose The Annotated Alice was published in 1960, followed by a sequel More Annotated Alice in 1990, perhaps the first scholar to look in depth for possible mathematical inspirations for Alice was Helena Pycior of the University of Wisconsin-Milwaukee, who in 1984 linked the trial of the Knave of Hearts with a Victorian book on algebra. Now Melanie Bayley, of the University of Oxford in England, has taken the analysis a lot further. She described her findings (well, since we are in the realm of literary interpretation here, I'd better say "her theory") in an article titled Alice's adventures in algebra: Wonderland solved, published in New Scientist, 16 December 2009.

Before I relate what Bayley has to say, let me summarize the history of Carroll's Alice in Wonderland.

In 1862, Dodgson, together with the Reverend Robinson Duckworth, rowed in a boat up the River Thames with three young girls, Lorina Charlotte Liddell, aged 13, Alice Pleasance Liddell, aged 10, and Edith Mary Liddell, aged 8, the daughters of Henry George Liddell, the Vice-Chancellor of Oxford University and Dean of Christ Church College, as well as headmaster of the nearby, private, Westminster School.

The journey started at Folly Bridge near Oxford and ended five miles away in the village of Godstow. As they rowed, Dodgson made up and told the girls a story about a bored little girl named Alice who goes looking for an adventure. The three girls loved it, and Alice Liddell asked Dodgson to write it down for her. Two years later he did just that, and on 26 November 1864 he gave Alice the handwritten manuscript of what he then called "Alice's Adventures Under Ground," illustrated by his own drawings.

Most of the story was based on situations and buildings in Oxford and at Christ Church. For example, the "Rabbit Hole" down which Alice descends to begin her adventure symbolized the actual stairs in the back of the college's main hall.

A year later, Dodgson - now masquerading as Lewis Carroll - published a greatly expanded version under the title "Alice's Adventures in Wonderland," with illustrations drawn by John Tenniel. It is in the new material he added, which includes the Cheshire Cat, the trial, the Duchess's baby, and the Mad Hatter's tea party, that we find allusions to mathematics. (Tweedledum, Tweedledee, Humpty Dumpty and the Jabberwock appear in the sequel, Alice Through the Looking-Glass.)

The book rapidly became a bestseller, it has never been out of print since it first appeared, and it has been translated into well over 100 languages.

So what does Bayley tell us about the mathematical ideas that Dodgson took inspiration from?

Now we get to the math part

First, we have to remind ourselves of what was going on in mathematics in the latter half of the nineteenth century, when Dodgson wrote his story. It was a turbulent period for mathematicians, with the subject rapidly becoming more abstract. The discoveries of non-Euclidean geometries, the development of abstract (symbolic) algebra that was not tied to arithmetic or geometry, and the growing acceptance - or at least use - of "imaginary numbers" were just some of the developments that shook the discipline to its core. By all accounts, Dodgson held a very traditionalist view of mathematics, rooted in the axiomatic approach of Euclid's Elements. (He was not a research mathematician, rather he tutored the subject.) Bayley describes him as a "stubbornly conservative mathematician," who was dismayed by what he saw as the declining standards of rigor. The new material Dodgson added to the Alice story for publication, she says, was a wicked satire on those new developments.

Perhaps the most obvious example is the Cheshire Cat, which disappears leaving only its grin, an obvious reference - critical in Dodgson's case - to increasing abstraction in the discipline.

For a more focused example, take the chapter "Advice from a caterpillar." Alice has fallen down the rabbit hole and eaten a cake that has shrunk her to a height of just 3 inches. The Caterpillar enters, smoking a hookah pipe, and shows Alice a mushroom that can restore her to her proper size. But one side of the mushroom stretches her neck, while another shrinks her torso, so she must eat exactly the right balance to regain her proper size and proportions. Bayley believes this expresses Dodgson's view of the absurdity of symbolic algebra.

The first clue, she says, may be the pipe. The word "hookah" is of Arabic origin, like "algebra". More to the point, the original Arabic term for algebra, widely known and used in the mathematical community in Dodgson's time, was al jebr e al mokabala or "restoration and reduction" - which exactly describes Alice's experience. Restoration was what brought Alice to the mushroom: she was looking for something to eat or drink to "grow to my right size again," and reduction was what actually happened when she ate some: she shrank so rapidly that her chin hit her foot.

Bayley suggests that the overall madness of Wonderland reflects Dodgson's views on the dangers of this new symbolic algebra. Alice has moved from a rational world to a land where even numbers behave erratically. In the hallway, she tries to remember her multiplication tables, but they have slipped out of the base-10 number system she is used to.

In the caterpillar scene, Alice's height fluctuates between 9 feet and 3 inches. Alice, bound by conventional arithmetic where a quantity such as size should be constant, finds this troubling: "Being so many different sizes in a day is very confusing," she complains. "It isn't," replies the Caterpillar, who lives in this absurd world.

The Caterpillar's warning, at the end of this scene, is perhaps one of the most telling clues to Dodgson's conservative mathematics, Bayley suggests. "Keep your temper," he announces. Alice presumes he's telling her not to get angry, but although he has been abrupt he has not been particularly irritable at this point, so it's a somewhat puzzling thing to say. But the word "temper" has another meaning of "the proportion in which qualities are mingled." So the Caterpillar could well be telling Alice to keep her body in proportion - no matter what her size. This may be another reflection of Dodgson's love of Euclidean geometry, where absolute magnitude doesn't matter: what's important is the ratio of one length to another. To survive in Wonderland, Alice must act like a Euclidean geometer, keeping her ratios constant, even if her size changes.

Of course, she doesn't. She swallows a piece of mushroom and her neck grows like a serpent with predictably chaotic results - until she balances her shape with a piece from the other side of the mushroom. This is an important precursor to the next chapter, "Pig and pepper", where Dodgson parodies another type of geometry. By this point, Alice has returned to her proper size and shape, but she shrinks herself down to enter a small house. There she finds the Duchess in her kitchen nursing her baby, while her Cook adds too much pepper to the soup, making everyone sneeze except the Cheshire Cat. But when the Duchess gives the baby to Alice, it turns into a pig.

According to Bayley, the target of this scene is projective geometry, a subject that involved concepts that Dodgson would have found ridiculous, particularly the "principle of continuity." Jean-Victor Poncelet, the French mathematician who set out the principle, described it as follows: "Let a figure be conceived to undergo a certain continuous variation, and let some general property concerning it be granted as true, so long as the variation is confined within certain limits; then the same property will belong to all the successive states of the figure."

When Poncelet talked of "figures", he meant geometric figures, of course, but Dodgson playfully subjects Poncelet's description to strict logical analysis and takes it to its most extreme conclusion. He turns a baby into a pig through the principle of continuity. Importantly, the baby retains most of its original features, as any object going through a continuous transformation must. His limbs are still held out like a starfish, and he has a queer shape, turned-up nose and small eyes. Alice only realizes he has changed when his sneezes turn to grunts.

The baby's discomfort with the whole process, and the Duchess's unconcealed violence, signpost Dodgson's virulent mistrust of "modern" projective geometry, Bayley says. Everyone in the pig and pepper scene is bad at doing their job. The Duchess is a bad aristocrat and an appallingly bad mother; the Cook is a bad cook who lets the kitchen fill with smoke, over-seasons the soup and eventually throws out her fire irons, pots and plates.

Alice, angry now at the strange turn of events, leaves the Duchess's house and wanders into the Mad Hatter's tea party. This, Bayley surmises, explores the work of the Irish mathematician William Rowan Hamilton, who died in 1865, just after Alice was published. Hamilton's discovery of quaternions in 1843 was hailed as an important milestone in abstract algebra, since they allowed rotations to be calculated algebraically.

Just as complex numbers work with two terms, quaternions belong to a number system based on four terms. Hamilton spent years working with three terms - one for each dimension of space - but could only make them rotate in a plane. When he added the fourth, he got the three-dimensional rotation he was looking for, but he had trouble conceptualizing what this extra term meant. Like most Victorians, he assumed this term had to mean something, so in the preface to his Lectures on Quaternions of 1853 he added a footnote: "It seemed (and still seems) to me natural to connect this extra-spatial unit with the conception of time."

As Bayley points out, the parallels between Hamilton's mathematics and the Mad Hatter's tea party are uncanny. Alice is now at a table with three strange characters: the Hatter, the March Hare and the Dormouse. The character Time, who has fallen out with the Hatter, is absent, and out of pique he won't let the Hatter move the clocks past six.

Reading this scene with Hamilton's ideas in mind, the members of the Hatter's tea party represent three terms of a quaternion, in which the all-important fourth term, time, is missing. Without Time, we are told, the characters are stuck at the tea table, constantly moving round to find clean cups and saucers.

Their movement around the table is reminiscent of Hamilton's early attempts to calculate motion, which was limited to rotatations in a plane before he added time to the mix. Even when Alice joins the party, she can't stop the Hatter, the Hare and the Dormouse shuffling round the table, because she's not an extra-spatial unit like Time.

The Hatter's nonsensical riddle in this scene - "Why is a raven like a writing desk?" - may more specifically target the theory of pure time. In the realm of pure time, Hamilton claimed, cause and effect are no longer linked, and the madness of the Hatter's unanswerable question may reflect this.

Alice's ensuing attempt to solve the riddle pokes fun at another aspect of quaternions that Dodgson would have found absurd: their multiplication is non-commutative. Alice's answers are equally non-commutative. When the Hare tells her to "say what she means", she replies that she does, "at least I mean what I say - that's the same thing". "Not the same thing a bit!" says the Hatter. "Why, you might just as well say that 'I see what I eat' is the same thing as 'I eat what I see'!"

When the scene ends, the Hatter and the Hare are trying to put the Dormouse into the teapot. This could be their route to freedom. If they could only lose him, they could exist independently, as a complex number with two terms. Still mad, according to Dodgson, but free from an endless rotation around the table.

The sting in the tale

Even if you accept Bayley's suggestions - and obviously I am inclined to do so, at least overall, otherwise I would not have written about her work - you might think the mathematical inspirations for some of the scenes we read in Alice are nothing more than an interesting footnote. Think again, says Bayley. Without those mathematical undercurrents, it is highly unlikely that Dodgson's book(s) would have achieved lasting, international stardom. His original nursery tale, written for the ten-year-old Alice Liddell, she says, would have been unlikely to attract much attention.

Dodgson was most witty when he was poking fun at something, Bayley explains, and then only when the subject matter got him truly riled. He wrote two uproariously funny pamphlets, fashioned in the style of mathematical proofs, which ridiculed changes at the University of Oxford. In comparison, other stories he wrote besides the Alice books were dull and moralistic.

"I would venture that without Dodgson's fierce satire aimed at his colleagues," Bayley claims, "Alice's Adventures in Wonderland would never have become famous, and Lewis Carroll would not be remembered as the unrivalled master of nonsense fiction."

Put that in your hookah and smoke it.

Lewis Carrol storytelling style inspired Godel, Escher, Bach which is a great book on computer science concepts.

Notable editions

Through the Looking Glass. -- hypertext with color illustrations.

Alice Through the Looking Glass -- As part of Project Gutenberg , the text for "Through the Looking Glass" was made available electronically to the Internet. This is the directory to Hypertext version of "Through the Looking Glass", based on that electronic document. The original electronic document in tar/gzip is here.

Alice's Adventures in Wonderland and Through the Looking Glass

    Lewis Carroll / Mass Market Paperback / Published 1995
    Amazon price: $3.16 ~ You Save: $0.79 (20%)

Alice's Adventures in Wonderland and Through the Looking Glass : Nonsense, Sense, and Meaning (Twayne's Masterwork Studies, No 81)

    Donald Rackin / Hardcover / Published 1991

    Amazon price: : $29.00

The Complete Alice- with the Original Illustrations by Sir John Tenniel in Full Colour- Lewis Carroll, John Tenniel, Philip Pullman- 9781627794350- Books

There are many editions of Alice's Adventures in Wonderland, but none to rival The Complete Alice, a gorgeous new gift book celebrating one hundred and fifty years of Alice.

In 1865, Macmillan published the first edition of Lewis Carroll's Alice's Adventures in Wonderland, widely acknowledged as one of the most influential children's books of all time. Its equally famous sequel, Through the Looking-Glass and What Alice Found There, was published in 1872.

The Complete Alice brings together Lewis Carroll's two extraordinary stories in a single glorious volume. The original artwork has been lovingly restored. Both texts are complete and unabridged, including the rarely seen "deleted" episode The Wasp in a Wig. Also included is The Story of Alice, an exclusive sixteen-page account of the creation and first publication of Alice, told for younger readers and featuring material from Macmillan's rich historical archive. A foreword from Philip Pullman introduces this truly special gift edition.

The Annotated Alice- The Definitive Edition- Lewis Carroll, Martin Gardner, John Tenniel

The culmination of a lifetime of scholarship, The Annotated Alice is a landmark event in the rich history of Lewis Carroll and cause to celebrate the remarkable career of Martin Gardner.

For over half a century, Martin Gardner has established himself as one of the world's leading authorities on Lewis Carroll. His Annotated Alice, first published in 1959, has over half a million copies in print around the world and is beloved by both families and scholars―for it was Gardner who first decoded many of the mathematical riddles and wordplay that lay ingeniously embedded in Carroll's two classic stories, Alice's Adventures in Wonderland and Through the Looking Glass.

Forty years after this groundbreaking publication, Norton is proud to publish the Definitive Edition of The Annotated Alice, a work that combines the notes of Gardner's 1959 edition with his 1990 volume, More Annotated Alice, as well as additional discoveries drawn from Gardner's encyclopedic knowledge of the texts. Illustrated with John Tenniel's classic, beloved art―along with many recently discovered Tenniel pencil sketches―The Annotated Alice will be Gardner's most beautiful and enduring tribute to Carroll's masterpieces yet.

Color, two-tone, and black-and-white photos and illustrations throughout

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Alice's Adventures in Programming Language Theory Wonderland- A Short List of Computer Science-Programming-Mathematics Books in the Style of Lewis Carroll - Monadically Speaking- Adventures in Programming Language Theory
June 10, 2011 |

Once upon a time, an MIT professor reputedly claimed that Alice's Adventures in Wonderland was the best book on computer science.

While that opinion is subjective, there are a number of papers or publications related to computer science, programming, or mathematics that are written in a style that at least loosely resembles Carroll's work.

In fact, one of the first documents that I encountered in this classification was a paper that I encountered in the Sterling Memorial Library of my college that was an academic treatise analyzing the role of logic in the humor of works by Lewis Carroll. The paper was actually written to fulfill an academic requirement (I think that it was written as a thesis for either a Master of Arts of Master of Science degree, probably in philosophy), but was actually great fun to read.

Ever since encountering that paper, I have subconsciously been searching for similar papers and publications that were associated, in some manner, with the writing style of Lewis Carroll.

One of the first books that I encountered that was written in that style was Compared to What?: An Introduction to the Anaylsis of Algorithms, by Gregory J. E. Rawlins (for some reason, my comment on the book at has apparently been borrowed, without my permission, by Google as their official review without any credit; I am not sure whether to laugh or to be annoyed).

This book included numerous quotations and illustrations from works by Carroll, and, unlike many other textbooks on the design and analysis of algorithms, was written from the perspective that every problem at some point did not have a solution, and described the process that originally led up to the described algorithm.

I enjoyed this book enough to wrap it in kaleidoscopic wrapping paper, and kept it in my stock until eventually moving from New York to Tokyo (one day, I hope to acquire another new copy).

Another fun-to-read book that I encountered in this style was a book on the Scheme programming language, The Little Schemer, by Daniel P. Friedman and Matthias Felleisen.

The Little Schemer is actually an updated version of a previous work, The Little LISPer, also by Daniel P. Friedman and Matthias Felleisen, which had focused on recursion in Lisp. Scheme is an alternative dialect with a cleaner syntax and such changes as hygienic macros and additional features as first-class continuations.

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The intention to make parallels between L. Carroll and S.Beckett and proposes an intertextual approach to show how much Caroll`s work can be interpreted as a foreshadowing of postmodern discourse in modern drama with specific reference to Beckett's. Carroll`s works tend to show certain interesting aspects that were to interest Beckett in his drama and postmodern concepts with regard to meaning of language, space and time, the problem of personal identity.Carroll prefigures modern drama, especially in the guise of the Theatre of the Absurd, and provides fertile ground for postmodern discourse - a radically new notion of setting, time, action, language, dialogue and plot.

Man is seen as disintegrated and his society presented as increasingly deconstructing and irrecoverably fragmented. This absurd image of man is not unconnected to Carroll's philosophy of nonsense which significantly engages questions of life and existence.

The sections of the paper is structured as follows; the significance of language, space and time, characters and the question of identity.

Space and time are undeniably important aspects of the Carroll stories. The space-time theme takes a complicated and more philosophical turn in Beckett's plays - actually indicates the caged nature of the world and nothingness in time. There are number of characters in Carroll's stories that prefigure Beckett's treatment of characters.

Their verbal exchange only point to the difficulty of codifying possible meanings and, like Beckett's characters, they seem to have no society, no history, no occupation, no real personality or identity except their names, that helps to generate incomprehensibility and indeterminacy



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